* Sheinbaum wins landslide to become first woman Mexican president

* India shares at record high, exit polls predict Modi landslide

* Moody's: SA coalition govt could complicate policy execution

* MSCIEF set for best day since mid Nov

June 3 (Reuters) - Emerging market stocks and currencies bounced back on Monday, with local elections in Mexico, India and South Africa and expected monetary policy easing from major central banks at the top of investors' radar.

The MSCI index for EM stocks climbed 2.1%, set for its biggest one-day jump since mid November, after having lost nearly 4% in four straight sessions. The currencies gauge edged 0.1% higher after three days of losses.

Traders largely expect interest rate cuts from the European Central Bank and the Bank of Canada this week, while U.S. rate reductions are expected later this year.

On the election front, Claudia Sheinbaum won a landslide victory to become Mexico's first female president. The Mexican peso weakened over 1% against the dollar as the ruling coalition looked poised for a super-majority that markets fear could bring constitutional reforms.

"(A super majority) would enable Sheinbaum and Morena (party) to push through constitutional amendments. Policy continuity will largely prevail under a Sheinbaum government, particularly when it comes welfare policy," Jason Tuvey, deputy chief EM economist at Capital Economics wrote.

"The next key thing to watch will be whether Sheinbaum offers any hints of cabinet appointments."

In India, exit polls pointed to a third term and sizable mandate for Prime Minister Narendra Modi, with investors eying public spending to maintain economic momentum, sending the country's stocks to record highs, the rupee up and bond yields lower.

Final results from South Africa's National Assembly elections confirmed that the ANC suffered its worst election showing since it came to power 30 years ago.

The South African rand strengthened 0.7% against the dollar, after slipping on Friday on fears the ANC could form a coalition with radical parties. The wider equity index jumped 1.3% after recent declines.

Moody's ratings agency said a coalition government could complicate the execution of fiscal, economic and social policies that would help address the South Africa's structural credit weaknesses.

On the data front, Central European manufacturing mostly contracted in May as Polish and Czech producers faced declining output and orders, while Hungarian factory activity stayed muted. S&P Global's Polish PMI fell to 45.0 in May from 45.9 in April, staying below the 50 mark for the 25th month in a row.

The Hungarian forint fell to a one-month low against the euro, as central Europe's markets awaited fresh data to gauge prospects of interest rate cuts ahead.

However, Budapest's blue-chip stocks index and Warsaw were up 2.2% and 1%, respectively.

HIGHLIGHTS:

** China factory activity growth hits 2-year high- Caixin PMI; Moody's raises China's growth forecast

** Turkey inflation hits 75% in expected peak before relief

** Iran's ex-President Ahmadinejad to run in presidential election- state TV

** Pakistan inflation slows to 11.8% in May, lowest in 30 months

(Reporting by Ankika Biswas in Bengaluru; Editing by Sriraj Kalluvila)